Why is intensity required here?

Q)A point source of light is placed at the centre of curvature of a hemispherical surface. The radius of curvature is r and the inner surface is completely reflecting. Find the force on the hemisphere due to the light falling on it if the source emits a power W.

I tried attempting this question as follows:$$F=frac{Delta p}{Delta t}$$
$$F= frac{2E}{cDelta t}$$
(since $p=frac{h}{lambda}$ and $E=frac{hc}{lambda}$)
$$=frac{2WDelta t}{cDelta t} $$
$$F=frac{2W}{c}$$

However, this answer is wrong and is correctly attempted as follows:

$$I=frac{W}{4pi r^2}$$
$$dE=frac{I ds}{4pi r^2}$$
$$dF=frac{dE}{C}$$
By symmetry net force on hemisphere is along x,
$$dF=intfrac{2WdA costheta}{4pi r^2c}$$
$$dF=frac{2W int dA cos theta}{4pi r^2c}$$
$$dF=frac{W}{2c}$$
Which is different from what I attempted. Why is intensity taken in the official answer and why is my answer wrong?